Theory of structured multiphase mixtures
type: Item
instance of: scholarly article
title: Theory of structured multiphase mixtures
zbMATH Open document ID: 0783.73002
author: Flavio Dobran
published in: Lecture Notes in Physics
publication date: 1993-01-23T00:00:00Z
review text: This work deals with multiphase mixtures characterized by interfaces between phases as opposed to single phase, multicomponent mixtures. Continuum field equations are used for each phase volume, the boundary conditions between the phases being provided by another set of field equations. Averaging of local macroscopic equations is taken over suitable time and space segments and the averaged variables appear in the mixture dynamics and energetics. Structural characteristics are accounted for by additional transport equations leading to additional balance equations. There is overlap with single phase, multi-component mixture theories only in special situations. The book is self-contained in that it contains an appendix in which relevant results on linear vector spaces, vector calculus and tensor representation theorems are quoted. It is comprised of eight chapters: Chapter 1: Historical developments of the subject are outlined. Chapters 2 and 3: The basic mechanical and thermodynamic field equations are developed in chapter 2 and enhanced in chapter 3 by additional transport equations to account for `structure'. Chapter 4: Restrictions imposed on the kinematic, dynamic and thermodynamic variables by the principle of material frame indifference are discussed. Chapter 5: A simplification of the theory is introduced by restricting the motion of a material phase volume to a rotation about its centre of mass and an affine deformation, relative to the same point, which is a pure dilatation. The results are compared with other existing theories of structured multiphase mixtures. Chapter 6: The principles of constitutive theory are developed for different types of mixtures, such as solid and fluid phases. Chapters 7 and 8: Particular constitutive equations are studied and results for two phase mixtures obtained.
Mathematics Subject Classification ID: 74-02
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 76A02
zbMATH DE Number: 108209
zbMATH Keywords: interfaces
zbMATH Keywords: averaged variables
zbMATH Keywords: additional transport equations
zbMATH Keywords: additional balance equations
zbMATH Keywords: thermodynamic field equations
zbMATH Keywords: principle of material frame indifference
zbMATH Keywords: material phase volume
zbMATH Keywords: constitutive equations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 108209